In "Romeo and Juliet", what are the links between Tybalt and Mercutio's deaths and Paris's death?

In addition to the information above, the deaths are also the result of impetuous behavior on the parts of all three young men.

Mercutio provokes Tybalt into a fight after Romeo refuses to be baited by Tybalt's goading. Romeo comes between the two and Mercutio is made "a grave man".  Romeo's passion gets the better of him when his friend is killed and seeks vengeance upon Tybalt. His passion again comes into play against Paris, who was just paying his respects to his "dead" betrothed.

The saddest part is that Mercutio and Paris were not even members of the feuding families, but rather relatives of the Prince.

One could almost call Paris an "innocent bystander" due to his ignorance of the whole situation. He was not involved in the feud in any way other than as an observer and suitor for Juliet.